How can i stop the fingers from stretching when i move the body in the Minecraft Rig?
this is most likely because you're currently selecting the mesh/skin when trying to move the character.

Instead you need to select those bones in order to move/rotate/scale the character.

This tutorial might help, https://youtu.be/_C3CCz5S75A?t=7m56s (at 7:56)
To move the whole character in while in pose mode, select and move that larger platform around his feet.